# Worksheet on Application of Factor Theorem

Practice the questions given in the worksheet on application of Factor Theorem.

1. Find the roots of the equation 6z$$^{2}$$ + 11z -10 = 0. Hence, factorize 6z$$^{2}$$ + 11z -10.

2. Find the roots of the equation 2m$$^{2}$$ - 3m - 6 = 0. Hence, factorize 2m$$^{2}$$ - 3m - 6 = 0

3. Find the roots of the equation p(p + 1) - 4 = 0. Hence, factorize 4 - p - p$$^{2}$$.

4. Find the quadratic equation whose roots are

(i) -3, 7

(ii) 2 + √3, 2 - √3

(iii) $$\frac{1}{√3}$$, - $$\frac{1}{√3}$$

5. Find the cubic equation whose roots are

(i) 1, 2, 3

(ii) -4, √3, -√3

(iii) $$\frac{1}{2}$$, $$\frac{√5}{2}$$, $$\frac{-√5}{2}$$

Answers for the worksheet on application of Factor Theorem are given below:

1. $$\frac{2}{3}$$ , $$\frac{-5}{2}$$; (3z - 2)(2z + 5)

2. $$\frac{3 + √57}{4}$$, $$\frac{3 - √57}{4}$$; (2m - $$\frac{3 + √57}{2}$$)(m - $$\frac{3 - √57}{4}$$)

3. $$\frac{-1 + √17}{2}$$, $$\frac{-1 - √17}{2}$$; ($$\frac{-1 + √17}{2}$$ - p)( $$\frac{1 + √17}{2}$$ + p)

4. (i) y$$^{2}$$ - 4y -21 = 0

(ii) z$$^{2}$$ - 4z + 1 = 0

(iii) 3p$$^{2}$$ - 1 = 0

5. (i) z$$^{3}$$ - 6z$$^{2}$$ + 11z - 6

(ii) m$$^{3}$$ + 4m$$^{2}$$ - 3m - 12

(iii) 8k$$^{3}$$ - 4k$$^{2}$$ - 10k + 5 = 0

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